Question

If `int1/((x^2 - 1)) log((x - 1)/(x + 1))dx = A[log((x - 1)/(x + 1))]^2 + c,` then ______

Options

• `1/2`

• `1/3`

• `1/4`

• `1/6`

Answer 1

If `int1/((x^2 - 1)) log((x - 1)/(x + 1))dx = A[log((x - 1)/(x + 1))]^2 + c,` then `underline(1/4)`.

Explanation:

Let I = `intlog((x - 1)/(x + 1)) . 1/(x^2 - 1)dx`

Put `log((x - 1)/(x + 1)) = t`

∴ `(1/(x - 1) - 1/(x + 1))dx = dt`

∴ `1/(x^2 - 1) dx = 1/2dt`

∴ I = `intt.1/2 dt = 1/4 t^2 + c`

= `1/4[log((x - 1)/(x + 1))]^2 + c`

∴ A = `1/4`